Question: Simplify the following expression: $y = \dfrac{-36a - 63}{-63a}$ You can assume $a \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-36a - 63 = - (2\cdot2\cdot3\cdot3 \cdot a) - (3\cdot3\cdot7)$ The denominator can be factored: $-63a = - (3\cdot3\cdot7 \cdot a)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $y = \dfrac{(9)(-4a - 7)}{(9)(-7a)}$ Dividing both the numerator and denominator by $9$ gives: $y = \dfrac{-4a - 7}{-7a}$